As the last remark, there is a possibility of the NESS behavior being quasi-stationary, which otherwise has been observed in different many-body systems with long-range interactions [1]}, [2]}. In such a case, the NESS clouds would eventually evolve into other stable configurations. The timescales for that would, however, need to exceed 5 seconds, given this is the longest duration of our simulations. For comparison, such timescales are much longer than the damping period of MOT clouds, taking some tens of milliseconds.
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